Understanding Quadratic Functions and Zeros

This video tutorial teaches how to graph quadratic functions and determine their zeros. It covers substitution and evaluation of quadratic equations, creating tables of values for graphing, and identifying zeros on graphs. The tutorial also addresses common misconceptions about zeros and demonstrates solving for zeros algebraically. Symmetry in quadratic graphs is also discussed.

What is the primary goal when graphing a quadratic function?

• To find the y-intercept

• To calculate the derivative

• To identify the zeros

• To determine the slope

When substituting x = 1 into the function y = 2x^2 - 3x + 1, what is the resulting value of y?

• 0

• 3

• 1

• 2

What is the value of y when x = 2 in the function y = 2x^2 - 3x + 1?

• 5

• 0

• 1

• 3

Which x-value results in a y-value of zero for the function y = x^2 + 2x - 8?

• 4

• 2

• -2

• 0

Which point on the graph of y = x^2 + 2x - 8 is a zero?

• (0, -8)

• (1, -5)

• (-4, 0)

• (2, 0)

What is a common misunderstanding about zeros in a table of values?

• Zeros are the same as the vertex

• Zeros always occur at the y-intercept

• Zeros must cross the x-axis

• Zeros are always positive

How do you find zeros algebraically for the function f(x) = -2x^2 + 7?

• Set f(x) to 7

• Set x to 7

• Set f(x) to 0

• Set x to 0

What is the approximate value of the zeros for the function f(x) = -2x^2 + 7?

• ±1.87

• ±2.87

• ±3.87

• ±0.87

What property of quadratic graphs allows them to be folded in half symmetrically?

• Their y-intercept

• Their axis of symmetry

• Their vertex

• Their linearity

What is the y-value when x = 0 for the function f(x) = -2x^2 + 7?

• -7

• 2

• 7

• 0